The Practice of Statistics for AP*, 4th Edition Glossary
Chapter 2
The 68-95-99.7 Rule Also known as the "empirical rule." In the Normal distribution
with mean μ and standard deviation σ, (a) Approximately 68% of the observations fall
within σ of the mean μ, (b) Approximately 95% of the observations fall within 2σ of μ,
and (c) Approximately 99.7% of the observations fall within 3σ of μ.
Cumulative relative frequency graph Used to examine location within a distribution.
Cumulative relative frequency graphs begin by grouping the observations into equalwidth classes. The completed graph shows the accumulating percent of observations as
you move through the classes in increasing order.
Density curve A curve that (a) is always on or above the horizontal axis, and (b) has
exactly 1 area underneath it. A density curve describes the overall pattern of a
distribution. The area under the curve and above any interval of values on the horizontal
axis is the proportion of all observations that fall in that interval.
Mean of a density curve The point at which the curve would balance if made of solid
material.
Median of a density curve The point with half the area under the curve to its left and
the remaining half of the area to its right.
Normal curves An important class of density curves that are symmetric, single-peaked,
and bell-shaped.
Normal distribution Described by a Normal density curve. Any particular Normal
distribution is completely specified by two numbers, its mean μ and standard deviation σ.
The mean of a Normal distribution is at the center of the symmetric Normal curve. The
standard deviation is the distance from the center to the change-of-curvature points on
either side. We abbreviate the Normal distribution with mean μ and standard deviation σ
as N(μ, σ).
Normal probability plot Used to assess whether a data set follows a Normal
distribution. To make a Normal probability plot, (1) arrange the data values from
smallest to largest and record the percentile of each observation, (2) use the standard
Normal distribution to find the z-scores at these same percentiles, and (3) plot each
observation x against the corresponding z. If the points on a Normal probability plot lie
close to a straight line, the plot indicates that the data are approximately Normal.
Pth percentile The value with p percent of the observations less than it.
Standard Normal distribution The Normal distribution with mean 0 and standard
deviation 1.
© BFW Publishers 2011
The Practice of Statistics for AP*, 4th Edition Glossary
Standard Normal table (Table A) A table of areas under the standard Normal curve.
The table entry for each value z is the area under the curve to the left of z.
Standardized values (z-scores) If x is an observation from a distribution that has known
x − mean
mean and standard deviation, the standardized value of x is z =
.A
standard deviation
standardized value is often called a z-score.
© BFW Publishers 2011